Problem: Solve for $x$ and $y$ using substitution. ${-4x-5y = -8}$ ${y = -4x-8}$
Answer: Since $y$ has already been solved for, substitute $-4x-8$ for $y$ in the first equation. ${-4x - 5}{(-4x-8)}{= -8}$ Simplify and solve for $x$ $-4x+20x + 40 = -8$ $16x+40 = -8$ $16x+40{-40} = -8{-40}$ $16x = -48$ $\dfrac{16x}{{16}} = \dfrac{-48}{{16}}$ ${x = -3}$ Now that you know ${x = -3}$ , plug it back into $\thinspace {y = -4x-8}\thinspace$ to find $y$ ${y = -4}{(-3)}{ - 8}$ $y = 12 - 8$ $y = 4$ You can also plug ${x = -3}$ into $\thinspace {-4x-5y = -8}\thinspace$ and get the same answer for $y$ : ${-4}{(-3)}{ - 5y = -8}$ ${y = 4}$